Radio Emission Of The Sun and Planets – Zheleznyakov

Posted on December 23, 2021 by The Mitr

In this post, we will see the book Radio Emission Of The Sun and Planets by V. V. Zheleznyakov.

About the book

The task of present-day radio astronomy is to study extraterrestrial objects by means of the nature of the radio emission coming from them. Radio astronomy research is valuable for the significance of the results which greatly supplement the data of optical astronomy. It has also become a basic source of information on regions which, whilst they play a part in the generation, reflection or scattering of radio waves, make no significant contribution to the optical part of the spectrum.
This book presents a detailed dis­cussion and analysis of the radio emission of the Sun, the Moon and the planets, and is an attempt to fill a gap in the literature currently available. There is much contemporary interest in the observation and interpretation of the radio emissions from these bodies, and this work will be of considerable value both to radio and optical astronomers, and also to the theoretical physicists who seek greater understanding of the results obtained by the users of radio telescopes. There is an extensive bibliography which adds to the importance of this book as a work of reference.

The book was translated from Russian by H.S.H. Massey and was edited by J.S. Hey. The book was published in 1970.

Credits to original uploader.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

FOREWORD ix

FOREWORD TO THE ENGLISH EDITION xiii

CHAPTER I. PHYSICAL CONDITIONS OF THE SUN, MOON AND PLANETS 1

1. The Sun’s Atmosphere 1

The chromosphere (2).
The corona (3)

2. Solar Activity 8

Plages and flocculi (8).
Sunspots (9).
Flares (12).
Coronal condensations (14)

3. The Moon and Planets 15

Mercury, Venus and Mars (15).
Jupiter and Saturn (17).
The Moon (18)

CHAPTER II. BASIC CHARACTERISTICS OF EXTRATERRESTRIAL RADIO
EMISSION AND METHODS FOR STUDYING THEM 20

4. Frequency Spectrum 21

Aerial temperature and effective temperature of radio emission (23).
Studying the radio-emission frequency spectrum. Multi-channel receiving devices and radio spectrographs (27)

5. Angular Spectrum 30

Aerial system requirements in radio astronomy. Parabolic aerials (30).
The two-element interferometer (31).
Modifications of the two-element interferometer (33).
The problem of studying the radio brightness distribution over a source. Variable-baseline interferometer (36).
The multiple-element interferometer (39).
The Mills Cross (42).
Eclipse observations (44)

6. Polarization of Radio Emission 46

Polarization parameters (46).
Methods of polarization measurements in the metric waveband (51).
Polarization measurements in the centimetric band (59)

7. Effect of the Earth’s Atmosphere on the Observed Radio 63

Emission Absorption of radio waves in the troposphere (63). Absorption of radio waves in the ionosphere (64). Effects connected with refraction of radio waves in the atmosphere (65).
Polarization
change of the radio emission as it passes through the ionosphere (68)

CHAPTER III. RESULTS FROM OBSERVATIONS OF THE RADIO EMISSION OF THE “QUIET” SUN 73

8. Frequency Spectrum of the “Quiet” Sun’s Radio Emission 74

Determining the level of the “quiet” Sun’s radio emission (74).
Observed dependence of Tes on wavelength (77)

9. Distribution of Radio Brightness over the Sun’s Disk 83

Remarks on methods of investigation. Some preliminary data (83).
Features of the T. distribution over the disk of the “quiet” Sun in the radio-frequency band (86)

CHAPTER IV. RESULTS OF OBSERVATIONS OF THE SUN’S SPORADIC RADIO EMISSION 99

10. The Slowly Varying Component 101

General characteristics. Correlation of the radio-emission flux with sunspots (101).
Position, form and size of local sources (102).
Radio-emission frequency spectrum (110).
Directional properties and polarization (113).
Altitude of local sources above the photosphere. Connection with optical features of the solar corona (116)

11. Microwave Bursts 120

General characteristics. Basic types of microwave bursts (120).
Frequency spectrum of bursts (125).
Polarization of radio emission (128).
Microwave bursts and chromospheric flares (130)

12. Noise Storms (enhanced radio emission and type I bursts) 135

Time characteristics of noise storms (136).
Frequency spectrum (137).
Connection with optical features (139).
Directional features of the radio emission (143).
Size and position of radio-emission sources in the corona (144).
Polarization of noise storms (148)

13. Type II Bursts 154

General characteristics (154).
Harmonics of type II bursts (157).
Fine structure of type II bursts (165).
Frequency drift and its interpretation (167)

14. Type III Bursts 176

General characteristics (176).
Polarization of bursts (180).
Connection with optical phenomena (181).
Position and movement of an emitting region in the corona. Frequency drift of bursts (185).
U-bursts (191)

15. Types IV and V Radio Emission 194

Basic characteristics of type IV radio emission (194).
Type V bursts (201)

16. Other Forms of Burst 202

Decimetric continuum (202).
Rapidly drifting decimetric bursts (205).
Continuum storms (208).
The event of 4 November 1957 (210).
Wide-band bursts of short duration (212).
Reverse-drift pairs (212)

17. Sporadic Radio Emission and Geophysical Phenomena 215

Preliminary remarks (215).
Radio emission of the Sun and sudden ionospheric disturbances. Connection between microwave bursts and hard solar radiation (217).
Solar radio emission and magnetic storms with a sudden beginning. Properties of geoeffective corpuscular streams (223).
Radio emission of the Sun and polar blackouts. Connection between continuum-type radio emission and the appearance of energetic particles (230).
General picture of the Sun’s sporadic radio emission (237)

CHAPTER V. RESULTS OF OBSERVATIONS OF RADIO EMISSION OF THE PLANETS AND THE MOON 244

18. First Investigations into the Radio Emission of the Moon,
Planets and Comets 244

First study of the Moon and planets in the radio-frequency band (244).
Radio emission of comets (249)

19. Sporadic Radio Emission of Jupiter 250

Radio emission flux and its time dependence (250).
Frequency spectrum (253).
Polarization (257).
Local sources of sporadic radio emission, their period of rotation and position on Jupiter’s disk (258).
Directional features of radio emission and size of local sources (264).
Connection with solar activity (266)

20. Continuous Radio Emission of the Planets 269

Radio emission of Saturn (269).
Radio emission of Jupiter (270).
Radio emission of Mars (277).
Radio emission of Venus (277).
Radio emission of Mercury (283)

21. Radio Emission of the Moon 283

Preliminary remarks (283).
Frequency spectrum and phase dependence of the Moon’s radio emission (285).
Radio brightness distribution over the lunar disk (292)

 

CHAPTER VI. PROPAGATION OF ELECTROMAGNETIC WAVES IN THE SOLAR CORONA 297

22. Propagation of Electromagnetic Waves in an Isotropic Coronal
Plasma (approximation of geometrical optics) 298

Quasi-hydrodynamic method and approximation of geometrical optics (298).
Waves in an isotropic plasma (305)

23. Propagation of Electromagnetic Waves in a Magnetoactive
Coronal Plasma (approximation of geometrical optics) 318

Electromagnetic waves in a homogeneous plasma in the presence of a constant magnetic field (318).
Waves in a non-uniform magnetoactive plasma (325).
Faraday effect in the solar corona (329).
Depolarizing factors and the question of elliptical polarization of certain bursts of solar radio emission (334)

24. Coupling of Electromagnetic Waves in a Plasma and Polarization of Solar Radio Emission 342

Limiting polarization of emission leaving the coronal plasma (344).
Preliminary remarks on the effect of the coupling of waves in the region of a quasi-transverse magnetic field (350).
Calculations of coupling by the phase integral method (353).
Certain features of solar radio emission polarization and their interpretation on the basis of wave coupling in the region of a quasi-transverse magnetic field in the corona (365)

25. Coupling of Electromagnetic Waves and the Problem of the
Escape of Radio Emission from the Corona 373

Preliminary remarks (373).
Conversion of plasma waves into electromagnetic waves in a smoothly non-uniform isotropic plasma (376).
Wave coupling in a smoothly non-uniform magnetoactive plasma (385). Conversion of plasma waves into electromagnetic waves because of scattering on electron density fluctuations (391)

CHAPTER VII. GENERATION AND ABSORPTION OF ELECTROMAGNETIC WAVES IN THE SOLAR CORONA 408

26. Emission and Absorption of Electromagnetic Waves in an Equilibrium Plasma 408

Emission transfer equation (408).
Electromagnetic wave emission by individual particles (413). Absorption of electromagnetic waves in an isotropic plasma (430). Absorption of electromagnetic waves in a magnetoactive plasma (440). Gyro-resonance absorption in the solar corona (452)

27. Emission, Absorption and Amplification of Electromagnetic Waves in a Non-equilibrium Plasma 459

The kinetic equation method and the Einstein coefficients method. The problem of wave amplification and instability in a plasma (459)
Reabsorption and amplification of plasma waves in a non-equilibrium plasma with H, = 0 (quantum treatment) (471)
Amplification and instability of plasma waves in a non-equilibrium plasma with H, = 0 (classical treatment) (478)
Maximum amplitude and harmonics of amplified plasma waves (482)
Reabsorption and amplification of electromagnetic waves in a non-equilibrium magnetoactive plasma (487)
The appearance of plasma waves in shock wave fronts (501)

CHAPTER VIII. THEORY OF THE SUN’S THERMAL RADIO EMISSION 508

28. Theory of the “Quiet” Sun’s Radio Emission 511

Radio emission mechanism (511). Theory of the B-component
in the simplest model of the chromosphere and corona (513).
Interpretation of certain features in the distribution of the radio
brightness over the Sun’s disk on the basis of more complex
models of the corona and chromosphere (521). Construction of
a model of the solar atmosphere from radio data (531)

29. Origin of the Slowly Varying Component of the Sun’s Radio
Emission 538

Thermal nature of the S-component of the sporadic radio emission (538)
Bremsstrahlung mechanism of the local S-component sources above spots (542)
Magnetic-bremsstrahlung mechanism of slowly varying emission (551) Origin of radio emission of haloes and local sources above flocculi free of spots (563)

CHAPTER IX. THEORY OF THE SUN’S NON-THERMAL RADIO EMISSION 568

30. Generation of Continuum-type Sporadic Radio Emission 568

Origin of microwave bursts and certain phenomena accompanying them (569).
Origin of the enhanced radio emission connected with sunspots (579).
Mechanism of type IV radio emission (583)

31. Generation of Types I, II and III Bursts 589

Theory of type III bursts (590).
Mechanism of type II bursts (602)
Generation of type I bursts (606)

508 511 538 568 568 589 610

CHAPTER X. ORIGIN OF RADIO EMISSION OF THE PLANETS AND THE  MOON 610

32. Hypotheses on the Mechanism of Jupiter’s Sporadic Radio Emission 610

The “thunderstorm” hypothesis (610).
Mechanism of plasma oscillations (612).
Plasma hypothesis of the origin of Jupiter’s radio emission when the planet’s magnetic field is taken into account (616)

33. Origin of the Continuous Radio Emission of Jupiter and Saturn 624

Radiation belts as the source of Jupiter’s decimetric radio emission (629).
Conditions of generation of Saturn’s radio emission (631)

34. Sources of Venus’s Radio Emission 638

The “ionospheric” model (639).
The “hot” surface model (645)

35. Theory of the Moon’s Radio Emission 651

Basic relations (651).
Interpretation of the results of observations of the Moon’s radio emission and the physical characteristics of its surface (657)

 

REFERENCES 669

INDEX 693

Posted in astronomy, books, electronics, engineering, physics, soviet, technology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

The Applications Of Continued Fractions And Their Generalizations To Problems In Approximation Theory – Khovanskii

Posted on December 22, 2021 by The Mitr

In this post, we will see the book

The Applications Of Continued Fractions And Their Generalizations To Problems In Approximation Theory by A. N. Khovanskii.

About the book

This book on continued fractions is devoted to certain selected topics in the analytic theory, with particular emphasis on those aspects that deal with rational approximations to functions and with numerical applications and computations. This text contains a tremendous mass of valuable formulas in continued fraction theory. Due to this fact, it can be considered as a useful reference manual for such formulas as well as a text on methods for research in analysis and in computational work.
In the first chapter of the present work a short exposition of the analytic theory of continued fractions is given. Problems in the arithmetic theory of continued fractions are not considered in this book.
The second chapter is devoted to the continued fraction expansion (by the method of Lagrange) of some well known functions. All expansions given in this chapter are special cases of a general expansion derived at the beginning of the chapter.
In the third chapter there is a short consideration of further methods for deriving rational function approximations to functions, leading to a series of approximation formulae for computing certain well known functions.
In the fourth chapter are considered the generalized continued fractions proposed by Euler. Examples are quoted showing the possibility of further generalizations of continued fractions which permit the approximate solution of algebraic equations of arbitrary degree.

The book was translated from Russian by Peter Wynn was published in 1963.

Credits to original uploader.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

CHAPTER I
Certain Problems in the Theory of Continued Fractions

§ 1. Convergents  1
§ 2. Transformations of Continued fractions 9
§ 3. The Transformation of Series into Continued Fractions 23
§ 4. General Considerations in the Convergence Theory of Continued Fractions 31
§ 5. Convergence Tests for Continued Fractions with Positive Coefficients 42
§ 6. Convergence Tests for Continued Fractions with Arbitrary Coefficients 46
§ 7. Convergence Tests for Continued Reactions which are Periodic in the Limit 58

CHAPTER II
Continued Fraction Expansions of Certain Functions

§ 1. A Solution of a Certain Riccati Equation with the help of Continued Fractions 76
§ 2. Continued Fraction Expansions. of Binomial Functions 100
§ 3. The Continued Fraction Expansion of $\sqrt[x]{x}$ 109
§ 4. Continued Fraction Expansions of the Natural Logarithm 110
§ 5. Continued Fraction Expansions of $e^{x}$ 112
§ 6. Continued Fraction Expansions of the Inverse trigonometric and Hyperbolic Functions 114
§ 7. Continued Fraction Expansions for $\tan x$ ind $\tanh x$ 122
§ 8. The Continued Fraction Expansion of the Integral $\int_{0}^{x}\frac{dx}{1+x^{k}}$ 125
§ 9. The Solution of the Equations of Boole and Riccati with the help of Continued Fractions 130
§ 10. Continued Fractions and the Hypergeometric Series 133
§ 11. Continued Fraction Expansions of Prym’s Function 142
§ 12. The Continued Fraction Expansion of the Incomplete Gamma-Function 148

CHAPTER III
Further Methods for Obtaining Rational Function Approximations

§ 1. Obreschkoff’s Formula 151
§ 2. The Derivation of Rational Function approximations to Certain Functions with the Help of Obreschkoff’s Formula 155
§ 3. The Solution of Certain Difference Equations with the Help of Continued Fractions 159
§ 4. The Derivation of Rational Function Approximations by means of Iteration 163
§ 5. Table of Approximate Values of $e^{x}$ 165
§ 6. Table of Approximate Values of $\ln x$ 166
§ 7. Table of Approximate Values of $\tan x$ and $\tanh x$ 167
§ 8. Rational Function Approximations for $\sinh x$ and $\sin x$ 167
§ 9. Rational Function Approximations for cosh x and cos x 171
§ 10. Rational Function Approximations to the Error Function 174
§ 11. The Continued Fraction Expansion of Stirling’: 5 Series 175
§ 12. Rational Function Approximations for $\Gamma(1 + x)$ 177

CHAPTER IV
Generalized Continued Fractions

§ 1. The Computation of Square Roots with the Help of Matrices of the Second Order 182
§ 2. The Solution of Quadratic Equations with the Help of Matrices of the Second Order 188
$ 3. The Calculation of Cube Roots with the Help of Matrices 194
§ 4. The Calculation of Fourth Roots with the Help of Matrices 196
§ 5. The Calculation of Roots of Arbitrary Rational Order with the Help of a Matrix 198
§ 6. The Solution of Cubic Equations with the Help of Matrices 199
$ 7. The Solution of Equations of Higher Order with the Help of Matrices 201

LITERATURE IN THE RUSSIAN LANGUAGE ON THE GENERAL THEORY OF CONTINUED FRACTIONS 203

REFERENCES 204

SUPPLEMENTARY REFERENCES 210

INDEX 211

 

 

Posted in books, mathematics, soviet | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Mathematical Problems: An Anthology ( Pocket Mathematical Library Work Book 3) – Dynkin et al

Posted on December 21, 2021 by The Mitr

In this post, we will see the book Mathematical Problems: An Anthology ( Pocket Mathematical Library Work Book 3) by E. B. Dynkin; S. A. Molchanov; A. L. Rozental; A. K. Tolpygo.

About the book

Regardless of their difficulty, the problems in this collection will all yield to the methods of high school mathematics. No attempt has been made to arrange the problems in order of difficulty, and hence there is no need to solve them consecutively. Thus you can dip into the collection at any point and solve the problems in any order.

If you can’t solve a problem right away, don’t be in a hurry to look up the solution. However, if the problem continues to resist your efforts to solve it, you are then entitled to consult theHints and Answers section. The hints are often brief, but they will be enough to set you on the right track once you have grappled with the problem on your own. The solution should be studied even when you have managed to solve the problem yourself, since it may well turn out that there is an unsuspected gap in your solution. Moreover, the solutions given here often digress and point out interesting side issues.

The book was translated from Russian by Richard Silverman was published in 1969.

Credits to original uploader.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

Preface vii
Problems 1
Hints and Answers 20
Supplementary Problems 65

Posted in books, mathematics, problem books, soviet | Tagged , , , , , , , , , , , , , , , , | 1 Comment

Learn Limits Through Problems! ( Pocket Mathematical Library Workbook 2) – Gelfand et al.

Posted on December 20, 2021 by The Mitr

In this post, we will see the book Learn Limits Through Problems! ( Pocket Mathematical Library Workbook 2) by S. I. Gelfand; M. L. Gerver; A. A. Kirillov; N. N. Konstantinov; A.G. Kushnirenko.

About the book

This is the second workbook in the Pocket Mathematical Library. It is essentially a programmed text inviting you to learn about limits (a key concept of modern mathematics) by solving a series of 56 problems and reading a little interspersed text. The problems are for the most part equipped with hints and answers (or both), enough for you to get the hang of them (harder problems are marked with asterisks). Moreover, the problems fall into three groups. The first, called “Preli­minaries,” puts you into the right frame of mind for absorbing the limit concept. The second, called “Concepts,” presents the irreducible amount of theoretical material needed to under­stand limits. The third, called “Calculations,” shows you how to evaluate limits once you know what they are.

The core of the book is really the section called “Solutions,” where all 56 problems are worked out in full detail. This section should be read carefully after you have tried solving the problems on your own. Please do not give up too soon, since this will only defeat the purpose of the book.

When you are satisfied that you have mastered the subject matter of the book, try solving the 11 problems in the section called “Test Problems.” These problems make up a little open- book examination, on which you should easily get a passing grade. Otherwise figure out where things went wrong and fill in the gaps in your knowledge. Don’t despair, because nobody finds the notion of a limit easy the first time around. Bon voyage!

The book was translated from Russian by Richard Silverman and was published in 1969.

Credits to original uploader.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

Preface vii

Problems 1

Group 1 (Preliminaries) 1
Group 2 (Concepts) 6
Group 3 (Calculations) 14

Solutions 22
Test Problems 69

Posted in books, mathematics, problem books, soviet | Tagged , , , , , , , , , , , , , | Leave a comment

Sequences and Combinatorial Problems ( Pocket Mathematical Library Workbook 1)- Gelfand et al

Posted on December 19, 2021 by The Mitr

In this post, we will see the book Sequences And Combinatorial Problems (Pocket Mathematical Library Workbook 1) by S. I. Gelfand; M. L. Gerver; A. A. Kirillov; N. N. Konstantinov; A.G. Kushnirenko.

About the book

This book has a very simple structure. It begins with a brief section called “Preliminaries” presenting the modicum of back­ground information needed to solve the 89 problems stated in the next section, called “Sample Problems.” These problems are, for the most part, equipped with hints or answers or both. But the nub of the book is the section called “Detailed Solutions,” where you will find all 89 sample problems worked out in full detail. In our opinion, just studying these solutions (after first spending a decent amount of time trying to solve the problems on your own!) is a perfectly plausible way of learning about sequences and combinatorial problems. Finally, to make sure you have mastered the subject matter of the book, you should attack all 37 problems in the section called “Test Problems.” In fact, think of this section as a (rather tough) final examination on which you must get at least a passing grade. Good luck!

The book was translated from Russian by Richard Silverman was published in 1969.

Credits to original uploader.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

Preface vii
Preliminaries 1
Sample Problems 8
Detailed Solutions 25
Test Problems 81

Posted in books, mathematics, problem books, soviet | Tagged , , , , , , , , , , , , , | 1 Comment

A Course of Mathematical Analysis (Vols 1 and 2) – Nikolsky

Posted on December 18, 2021 by The Mitr

In this post we will see the two volume Course in Mathematical
Analysis by S. M. Nikolsky.

About the book

The major part of this two-volume textbook stems from the
course in mathematical analysis given by the author for many
years at the Moscow Physico-technical Institute.

The first volume consisting of eleven chapters includes an
introduction (Chapter 1)which treats of fundamental notions of
mathematical analysis using an intuitive concept of a limit. With
the aid of visual interpretation and some considerations of a
physical character it establishes the relationship between the
derivative and the integral and gives some elements of differentiation and integration techniques necessary to those readers who are simultaneously studying physics.

The notion of a real number is interpreted in the first volume
(Chapter 2) on the basis of its representation as an infinite decimal. Chapters 3-11 contain the following topics: Limit of Sequence, Limit of Function, Functions of One Variable, Functions of Several Variables, Indefinite Integral, Definite Integral, Some Applications of Integrals, Series.

Volume 2 contains multiple integrals, field theory. Fourier series and Fourier integral, differential manifolds and differential forms, and the Lebesgue integral.

The books were translated from the Russian by V. M. Volosov. The
book was published by first Mir Publishers in 1977 with reprints in
1981, 1985 and 1987. The second volume below is from the 1987 print, while the first one is from 1977 one.

Note: Volume 2 is at a much better scan resolution. In an earlier post we had seen only Vol. 2, that post had dead links. This post with both volumes has cleaned scans and updated links. Earlier post has been updated.

Credits to the original uploaders.

You can get

Volume 1 here

and here

Volume 2 here

and here

 

Contents

Volume 1

Preface to the English Edition 5

Chapter 1. Introduction 13

Chapter 2. Real Numbers 45

Chapter 3. Limit of Sequence 68

Chapter 4. Limit of Function 90

Chapter 5. Differential Calculus. Functions of One Variable 127

Chapter 6. n-dimensional Space. Geometrical Properties of Curves 180

Chapter 7. Differential Calculus. Functions of Several Variables 215

Chapter 8. Indefinite Integral. Properties of Polynomials 314

Chapter 9. Definite Integral 351

Chapter 10. Some applications of integral. Approximate Methods 395

Chapter 11. Series 417

Name Index 453

Subject Index 455

Volume 2

Chapter 12. Multiple Integrals 9

Chapter 13. Scalar and Vector Fields. Differentiation and Integration
of Integral with Respect to Parameter. Improper Integrals 80

Chapter 14. Normed Linear Spaces. Orthogonal Systems 147

Chapter 15. Fourier Series. Approximation of Functions with Polynomials 188

Chapter 16. Fourier Integral. Generalized Functions 240

Chapter 17. Differentiable Manifolds and Differential Forms 289

Chapter 18. Supplementary Topics 326

Chapter 19. Lebesgue Integral  338

Name Index 437
Subject Index  438

 

Posted in books, mathematics, mir books, mir publishers, soviet | Tagged , , , , , , , , , , , , , , , , , , , , | 1 Comment

Thinking Machines – Gutenmacher

Posted on December 17, 2021 by The Mitr

In this post, we will see the book Thinking Machines by L. Gutenmacher.

About the book & the author

The book describes earliest computers, technologies and computing techniques and algorithms. The fundamental aspects of computation are well described in the book.
Gutenmacher was one of the earliest computer scientists in the Soviet Union. He pioneered the usage of computers to model cognitive and linguistic processes. His research papers covered such topics as data storage and retrieval, software development, and computerized telephony. A number of his works were translated into English, German, French, and Spanish.

The book was translated from Russian by A. Zdornykh and was designed by V. Yeryomin The book was published in 1960 by Foreign Languages Publishing House.

Original scan by DLI. Note: The scan is warped and not clear at places, but is mostly readable.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

General 3

Machines and Mechanisation 5
Specialisation and “Qualification” of Information and Logical Machines 9
Block Diagram of an Electronic Information and Logical Machine 12
Machine and Human Memory 14
Machine Problems 20
Machine Tests 25

Machine Memory 32

External Memory 32
Internal Memory 48
Long-time Capacity Memory 52
Inductive Long-time Memory 58
Photo-electronic Long-time Memory 59
Memory Elements of Volatile Memory 60
Magnetic Volatile Memory 64
Capacitive Volatile Memory 68

Machine Memory Address Systems 72

Multi-dimension Address System 72

Number Magnetic Address System 78

Associative (Word) Address System 87
Automatic Dictionary 91

Information Traffic in the Machine 96

Sequential-parallel Shifting of Information 96
Telelibrary 102
Information Machines and Telephone-telegraph Stations 108

 

Computer Elements Information Machines 115

“Logical” keys 115
Computer Units and Circuits 120

Machine Processing of Information 138

Machine Scientific and Technical Information 138
Machine Language 146
Processing Chemistry Literature 158
Processing Statistical and Planning Information 173

Posted in books, computers, engineering, foreign languages publishing, soviet, technology | Tagged , , , , , , , , , | 1 Comment

Eight Lectures on Mathematical Analysis – Khinchin

Posted on December 16, 2021 by The Mitr

In this post, we will see the book Eight Lectures On Mathematical Analysis by A. Ya. Khinchin.

About the book

 Eight Lectures on Mathematical Analysis is a translation and adaptation of a book by the outstanding Russian mathe­matician A. Ya. Khinchin. It is based on a series of lectures delivered at the University of Moscow by Professor Khinchin to improve the mathematical qualifications of engineers.
In this book, the reader will find a masterful outline of the fundamental ideas of mathematical analysis. Inessential de­tails have purposely been omitted, and the resulting exposition is clear and easy to follow. The book should be accessible to anyone who has had even a sketchy introduction to the mate­rial. And yet, because it is a concise, lucid exposition of the most important concepts of mathematical analysis, the book should be of value to the student enrolled in a university course in analysis.
A. YA. KHINCHIN, until his death in 1959, was a professor at Moscow State University, a corresponding member of the Academy of Sciences, and a member of the Academy of Pedagogical Sciences of the RSFSR. The author of more than one hundred fifty mathematical research papers and books, he will be remembered as a world-renowned authority in mathemati­cal analysis, probability theory, number theory, and mathe­matical statistics.

The book was translated from Russian by Irena Zygmud was published in 1965.

Credits to original uploader.

Note: This is one of the clearest exposition of these fundamental mathematical concepts that I have come across. Khinchin was a genius mathematician teacher who develops the concepts very gradually not assuming much and explains subtle points in the process which are usually missed out. Also, we never lose sight of what we are trying to achieve in a derivation with a clear logical path towards it and its consequences for the discussion.  I hope you enjoy this book as much as I did.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

LECTURE 1. The Continuum 1

1. Why begin with the continuum? 1
2. Need for a theory of real numbers 3
3. Construction of the irrational numbers 7
4. Theory of the continuum 11
5. Fundamental lemmas of the real number system 16

LECTURE 2. Limits 22

6. What is a limit? 22
7. Some ways of tending toward a limit 24
8. The limit of a constant function 27
9. Infinitely small and infinitely large quantities 28
10. Cauchy’s condition for the limit of a function 31
11. A remark on the fundamental theorems on limits 33
12. Partial limits; the upper and lower limits 33
13. Limits of functions of several variables 40

LECTURE 3. Functions 44

14. What is a function? 44
15. The domain of a function 49
16. Continuity of a function 50
17. Bounded functions 52
18. Basic properties of continuous functions 55
19. Continuity of the elementary functions 60
20. Oscillation of a function at a point 63
21. Points of discontinuity 65
22. Monotonic functions 67
23. Functions of bounded variation 69

LECTURE 4. Series 71

24. Convergence and the sum of a series 71
25. Cauchy’s condition for convergence 74
26. Series with positive terms 75
27. Absolute and conditional convergence 81
28. Infinite products 84
29. Series of functions 88
30. Power Series 96

LECTURE 5. The Derivative 102

31. The derivative and derivates 102
32. The differential 108
33. Lagrange’s theorem (first mean value theorem) 113
34. Derivatives and differentials of higher order 116
35. Limits of ratios of infinitely small and infinitely large quantities 118
36. Taylor’s formula 121
37. Maxima and minima 125
38. Partial derivatives 127
39. Differentiating implicit functions 132

LECTURE 6. The Integral 137

40. Introduction 137
41. Definition of the integral 138
42. Criteria for integrability 144
43. Geometric and physical applications 148
44. Relation of integration to differentiation 152
45. Mean value theorems for integrals 154
46. Improper integrals 158
47. Double integrals 164
48. Evaluation of double integrals 169
49. The general operation of integration 173

LECTURE 7. Expansion of functions in series 177

50. Use of series in the study of functions 177
51. Expansion in power series 179
52. Series of polynomials and the Weierstrass theorem 183
53. Trigonometric series 190
54. Fourier coefficients 192
55. Approximation in the mean 194
56. Completeness of the system of trigonometric functions 197
57. Convergence of Fourier series for functions with a bounded integrable derivative 201
58. Extension to arbitrary intervals 203

LECTURE 8. Differential Equations 206

59. Fundamental concepts 206
60. The existence of a solution 211
61. Uniqueness of the solution 220
62. Dependence of the solution on parameters 222
63. Change of variables 226
64. Systems of equations of higher orders 230

Posted in books, mathematics, soviet | Tagged , , , , , , , , , , , , , , , , , , , , , | 2 Comments

The Origin of Life – Oparin

Posted on December 15, 2021 by The Mitr

In this post, we will see the book The Origin of Life by A. I. Oparin.

About the book

This book discusses the ideas of origin of life on Earth. Alexander Ivanovich Oparin was a Soviet biochemist notable for his theories about the origin of life, and for his book The Origin of Life. He also studied the biochemistry of material processing by plants and enzyme reactions in plant cells.

The book discusses the possible bio-chemical pathways, complex organic molecules,  environmental conditions and geological factors for the origin and evolution of life. The book is a shortened version of his book The Origin of Life on Earth. On the whole, Oparin described a biochemical adventure marked by chemico-physics and natural selection, this latter working on microstructure. Oparin worked according to the canons of dialectic materialism applied to Nature by Friedrich Engels and did not give anything to divine and fantastic. In such context, proteins and enzymes were the dominant substances of life owing to their manifold activities

The book was translated from Russian was published in 1955  by Foreign Languages Publishing House. There are other translations as well notably by Dover published around the same time.

Credits to original uploader.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

CHAPTER ONE.
The Origin of Life—Materialism Versus Idealism and Religion 5

CHAPTER TWO.
The Primary Origin of the Most Element­ary Organic Substances—Hydrocarbons and Their Deriv­atives 21

CHAPTER THREE.
The Origin of Proto-Proteins 40

CHAPTER FOUR.
The Origin of Primary Colloidal For­mations 54

CHAPTER FIVE. The Organization of Living Protoplasm 64

CHAPTER SIX. The Origin of Primary Organisms 78

Conclusion 100

Posted in books, foreign languages publishing, geology, history, life sciences, popular science, soviet | Tagged , , , , , , , , , , , | Leave a comment

The Teaching of Mathematics – Essays by A. Ya. Khinchin

Posted on December 14, 2021 by The Mitr

In this post, we will see the book The Teaching of Mathematics by A. Ya. Khinchin.

About the book

Khinchin was a teacher-genius before his time and a mathematician of outstanding calibre. The main contents of this book are four articles written by A. Ya. Khinchin for Russian mathematics teachers. 101 pages are devoted to four articles written between 1938 and 1949 by Khinchin (who died in 1959), the remainder of the book to biographical notes and an appendix on mathematics teaching in the Soviet school.
One of the best sections is the one on the concept of limit. The author traces the historical development of the limit concept to determine which approach is best suited for the schools.
In his first article on basic concepts, Professor Khinchin stresses the basic importance of teaching so as not to conflict with later learning. He favors simplification, but never falsification. He advocates precise language
The second article on Mathematical Definitions is excellent and should be read by high school teachers. The discussion of the difference between a definition and a description and when it is desirable to present each is particularly good. It is refreshing that a mathematician of Khinchin’s standing had such understanding of teaching problems.

Some absolute gems of advice and insight to consider if you are in education. Though written 80 years back the ideas of Khinchin are very relevant now.

The book was edited by B. V. Gnedenko and was translated from Russian by W. Cochrane and D. Vere-Jones. The book was published in 1968.

Credits to original uploader.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

Introduction by Ian N. Sneddon vii
Translators’ Foreword ix

B. V. Gnedenko

Introduction to the Russian edition xiii
Note for the English edition xx

A. Ya. Khinchin

Basic Concepts of Mathematics in the Secondary Schools 1
Section 1 The Concept of Number 1
Section 2 The Concept of Limit 20
Section 3 The Concept of Functional Dependence 31
Mathematical Definitions in the Secondary Schools 44
On Formalism in School Mathematics Teaching 60
On the Educative Effect of Mathematics Lessons 77

Appendix 1

B. V. Gnedenko and A. I. Markushevich 102
A. Ya. Khinchin: A Biographical Sketch 113
Bibliography of Publications 115

Appendix 2

D. Vere-Jones
Mathematics Teaching and the Soviet School 117

List of General References 165

Popular Lectures in Mathematics: Edited by I. N. Sneddon 166

Topics in Mathematics: Edited by A. L. Putnam and I. Wirszup 167

Posted in books, mathematics, soviet | Tagged , , , , , , , , , , , | 1 Comment